Related papers: Reconstruction of Multidimensional Signals from Ir…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Electron microscopy has shown to be a very powerful tool to map the chemical nature of samples at various scales down to atomic resolution. However, many samples can not be analyzed with an acceptable signal-to-noise ratio because of the…
In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated…
Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…
Multi-view image acquisition systems with two or more cameras can be rather costly due to the number of high resolution image sensors that are required. Recently, it has been shown that by covering a low resolution sensor with a non-regular…
In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
An encryption of a signal ${\bf s}\in\mathbb{R^N}$ is a random mapping ${\bf s}\mapsto \textbf{y}=(y_1,\ldots,y_M)^T\in \mathbb{R}^M$ which can be corrupted by an additive noise. Given the Encryption Redundancy Parameter (ERP) $\mu=M/N\ge…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling…
In the present work, we propose a novel method for reconstruction of multi-dimensional kinetic distributions, based on their representation as a mixture of Dirac delta functions. The representation is found as a solution of an optimization…
The Mean Square Error (MSE) has shown its strength when applied in deep generative models such as Auto-Encoders to model reconstruction loss. However, in image domain especially, the limitation of MSE is obvious: it assumes pixel…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of…
Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
Fast spin-echo (FSE) pulse sequences for Magnetic Resonance Imaging (MRI) offer important imaging contrast in clinically feasible scan times. T2-shuffling is widely used to resolve temporal signal dynamics in FSE acquisitions by exploiting…